Related papers: Lattice Gauge Tensor Networks
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal…
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature,…
Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional…
We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative.…
We streamline and generalize the recent progress in understanding entanglement between spatial regions in Abelian gauge theories. We provide an unambiguous and explicit prescription for calculating entanglement entropy in a $\mathbb Z_N$…
We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric…
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints, and can be regarded as the low energy limit of an extended lattice model with a local symmetry. We propose a numerical…
Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
We propose a new point of view to gauge theories based on taking the action of symmetry transformations directly on the coordinates of space. Via this approach the gauge fields are not introduced at the first step, and they can be…
Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques,…
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…